Operations Managers Often Use Work Sampling to Estimate How Much $\quad y =$

Operations managers often use work sampling to estimate how much time workers spend on each operation. Work sampling-which involves observing workers at random points in time-was applied to the staff of the catalog sales department of a clothing manufacturer. The department applied regression to the following data collected for 40 consecutive working days: TIME: $\quad y =$ Time spent (in hours) taking telephone orders during the day
ORDERS: $\quad x _ { 1 } =$ Number of telephone orders received during the day
WEEK: $\quad x _ { 2 } = 1$ weekday, 0 if Saturday or Sunday
Consider the following 2 models:
Model 1: $E ( y ) = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } \left( x _ { 1 } \right) ^ { 2 } + \beta _ { 3 } x _ { 2 } + \beta _ { 4 } x _ { 1 } x _ { 2 } + \beta _ { 5 } \left( x _ { 1 } \right) ^ { 2 } x _ { 2 }$
Model 2: $E ( y ) = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 3 } x _ { 2 }$
What strategy should you employ to decide which of the two models, the higher-order model or the simple linear model, is better?

A) Compare the two models with a nested model $\mathrm { F }$ -test, i.e., test the null hypothesis, $H _ { 0 } : \beta _ { 2 } = \beta _ { 4 } = \beta _ { 5 } = 0$ .
B) Compare $R ^ { 2 }$ values; the model with the larger $R ^ { 2 }$ will always be the better model.
C) Compare the two models with a t-test, i.e., test the null hypothesis, $H _ { 0 } : \beta _ { 1 } = 0$ .
D) Always choose the more parsimonious of the two models, i.e., the model with the fewest number of $\beta$ -coefficients.